King and rook - insufficient material?

I'm pretty sure you can win king and rook vs king. I found myself in the weaker position in this scenario just a minute ago. However, my opponent had run out of time on the blitz setting and I assumed it was game to me. Yet chess.com declared a draw due to insufficient material. Is this a fault in the system or something I don't know about?

You only had the K which was insufficient material. If YOU had run out of time then he would have got the win due to K and R being able to win.

Because you can't win with just a king, it's a draw if he runs out of time. If you run out of time against someone who can checkmate you, it's your loss.

Would you checkmate your opponent with HIS rook?

It's an instance of a "Time vs Material" draw.  There are 4 forms of insufficient mating material:

Lone K

King and Bishop

King and Knight

King and Two Knights and your opponent specifically has no pawns left (he can still have pieces left).

King and Two Knights with a pawn of the opposite color, or any other combination of pieces not mentioned above is a win for the player with time still left on their clock.

Now this would be interesting to see with chess.com, whether they have this set up right or if this is a bug and it would reward Black with a draw if he let's his clock run out:

White is currently in check.  The only move for him is 1.Qxg8+, and after Black plays 1...Kxg8, by rule, White has insufficient mating material.  HOWEVER, that rule does have an exception in that if White can demonstrate "Forced" checkmate (NOT Helpmate), then he still wins if Black lets his clock run out.  So in this example, after 2.Bh6!!, if Black intentionally lets his clock run out, White should be awarded the win as the mate is 100% completely and utterly forced, namely 2...Kh8 (Only legal move) 3.Kf7 e5 (or 3...e6, same difference) 4.Bg7#

If chess.com awards a draw when Black's clock runs out, chess.com has a bug.  It it would reward White with the win, then it's functioning properly.

I have just finished a game in which my opponent ran out and the game was declared draw due to insufficient material though I was the one with rook and king. Is this possible?

It should not be possible. Can you link to the game?

In this game you were white and did not have the rook, you only had a king. Your opponent ran out of time, so the game was drawn.